Characteristic Penetration Length Research Articles

Interpenetration and Friction of Brush-Coated Surfaces under External Load: Analytical Theory and SCF Calculations

We studied the compression and interpenetration properties of two opposing monodisperse polymer brushes under external load by analytical theory and by a numerical self-consistent field (SCF) approach. Analytical expressions are proposed for the brush density profiles in the interpenetration zone and verified by numerical SCF calculations. We quantify the interpenetration of two opposing brushes by the characteristic penetration length and by two integral parameters: the overlap integral, Γ, representing the number of interbush contacts, and the number of brush monomer units in the foreign half-space, Σ. The interpenetration parameters are studied in two conjugate ensembles as functions of the brush separation and of the external pressure. We propose a theoretical description of the solvent-mediated friction force in the low shearing rate regime on the basis of the Brinkman equation for two compressed brushes sliding against each other. We demonstrate that the total friction force which also includes direct brush–brush friction is expressed in terms of Γ and Σ. The SCF data for the interpenetration parameters Γ and Σ and hence for the total sliding friction force in the pressure ensemble collapse onto universal master curves when rescaled by the factor (N/σ)1/3 as suggested by the theory, where N is the chain length and σ is the surface grafting density. Finally, we define the kinetic friction coefficient as a function of the external pressure and analyze its universal rescaled behavior in the two limits of nondraining and free-draining brushes.

The Princess and the Nanoscale Pea: Long-Range Penetration of Surface Distortions into Layered Materials Stacks.

The penetration of moiré out-of-plane distortions, formed at the heterogeneous interface of graphene and hexagonal boron nitride (h-BN), into the layered h-BN stack is investigated. For aligned contacts, the estimated characteristic penetration length of ∼4.7 nm suggests that even at the far surface of a ∼25 h-BN layer thick slab stacked atop the contact, a corrugation of ∼0.1 Å, well within experimental resolution, should still be clearly evident. The penetration length is found to strongly reduce with increasing misalignment angle of the graphene/h-BN junction, where the effect of thermal fluctuations conceals the moiré-induced corrugation in the bulk. These results can be rationalized by continuum elastic theory arguments for anisotropic media. Our findings, which are expected to generally apply for layered heterojunctions, may serve as a route to control the surface corrugation, adhesive properties, and tribological characteristics of two-dimensional materials.

High power density nuclear battery prototype based on diamond Schottky diodes

We report here for the first time a fabrication of betavoltaic battery prototype consisting of 200 single conversion cells based on Schottky barrier diamond diodes which have been vertically stacked with ~24% 63Ni radioactive isotope. The maximum electrical output power of about 0.93 μW was obtained in total volume of 5 × 5 × 3.5 mm3. We used the ion-beam assisted lift-off technique to obtain conversion cells of minimal thickness comparable with the characteristic penetration length of beta-particles emitted by 63Ni isotope. The obtained value of 15 μm was limited by the mechanical strength of produced structures and process reliability. To check the performance of thin diamond based conversion cells we carried out IV-curves measurements at electron beam irradiation in SEM. We found that the sacrificial layer for the splitting of such thin conversion cell from HPHT diamond substrate did not cause a considerable degradation of device charge collection efficiency. As a result, the fabricated prototype provided the output power density of about 10 μW/cm3, that is the best known value for nuclear batteries based on 63Ni radioisotope. Moreover, the long half-life of 63Ni isotope gives the battery specific energy of about 3300 mWh/g that is an order of magnitude higher than the typical value of commercial chemical cells.

Development of a 3-D visible limiter imaging system for the HSX stellarator.

A visible camera diagnostic has been developed to study the Helically Symmetric eXperiment (HSX) limiter plasma interaction. A straight line view from the camera location to the limiter was not possible due to the complex 3D stellarator geometry of HSX, so it was necessary to insert a mirror/lens system into the plasma edge. A custom support structure for this optical system tailored to the HSX geometry was designed and installed. This system holds the optics tube assembly at the required angle for the desired view to both minimize system stress and facilitate robust and repeatable camera positioning. The camera system has been absolutely calibrated and using Hα and C-III filters can provide hydrogen and carbon photon fluxes, which through an S/XB coefficient can be converted into particle fluxes. The resulting measurements have been used to obtain the characteristic penetration length of hydrogen and C-III species. The hydrogen λiz value shows reasonable agreement with the value predicted by a 1D penetration length calculation.

Characterization of the Pore Filling of Solid State Dye Sensitized Solar Cells with Photoinduced Absorption Spectroscopy

Near steady-state photoinduced absorption (PIA) and UV-Vis absorption spectroscopy are used to characterize the pore filling of spiro-MeOTAD (2,2′,7,7′-tetrakis-(N,N-di-p-methoxyphenylamine)9,9′-spirobifluorene) into the nanoparticulate TiO2electrode of a solid-state dye-sensitized solar cell (ssDSC). The volumetric ratio of filled to unfilled pore volumes, as well as the optical signature of interacting chemical species, that is, the hole-transfer yield (HTY), are investigated. PIA spectroscopy is used to measure the HTY, relative to the amount of spiro-MeOTAD present, without needing to determine the extinction coefficients of the dye and spiro-MeOTAD cation species. The Beer-Lambert law is used to relate the relative PIA signal to the penetration length of the hole-conductor in the TiO2film. For the sample thickness range of1.4–5 μm investigated here, the optimum characteristic penetration length is determined to be3.1+0.46 μm, which is compared to 1.4 μm for the 200 mgmL−1concentration of spiro-MeOTAD conventionally used. Therefore, doubling the effective penetration of spiro-MeOTAD is necessary to functionalize all the dye molecules in a ssDSC.

Competition effects in steady-state diffusion-limited reactions: Renormalization group approach

We consider the steady-state competition between perfectly absorbing sinks distributed uniformly in a spherical region. An equation for the coarse-grained concentration of diffusing particles inside the region is derived following the renormalization group approach. The total flux of diffusing particles, their coarse-grained concentration, and the characteristic penetration length are found. We then compare our results with so-called mean field approximation, and show that the latter approach cannot correctly describe the coarse-grained concentration in the system under consideration.

Simple and multiple scattering in disordered one-dimensional media: Renormalisation group approach

The exact characteristic penetration length ζ associated with both simple and multiple incoherent elastic scattering in semi-infinite one-dimensional disordered media is established as a function ofp (concentration of scattering centers) andf0 (transmission coefficient of a single center). Then we exhibit how these phenomena can be seen as critical ones, and the corresponding ζ are reobtained within convenient real space renormalisation group frameworks. Finally we discuss a generalized model where the single center transmission coefficientf can randomly take two different valuesf1 andf2.

Induced pretransitional Rayleigh-Bénard convection

We study the properties of subcritical Rayleigh-B\'enard rolls induced by a triggering velocity applied to one side of a fluid layer maintained in controlled subcritical conditions. The induced rolls are spatially damped exponentially with increasing distance from the position of the triggering velocity. We point out a remarkable critical behavior of a characteristic penetration length $\ensuremath{\xi} (\ensuremath{\xi}={\ensuremath{\xi}}_{0}{\ensuremath{\epsilon}}^{\ensuremath{-}\ensuremath{\nu}})$. The values of $\ensuremath{\nu}=0.50\ifmmode\pm\else\textpm\fi{}0.02$ and ${\ensuremath{\xi}}_{0}=(0.38\ifmmode\pm\else\textpm\fi{}0.01)d$ are in perfect agreement with those calculated according to the Landau-Hopf model.

Mode propagation in superconductors near Tc

The linearized Eliashberg theory for dirty superconductors in the vicinity of T c is used to generate the dynamic Ginzburg-Landau (GL) equation for the order parameter and the coupled Boltzmann equation for the quasi-particle distribution function, with and without magnetic impurities and inelastic phonon scattering. The Schmid and Schön (SS) separation of the order parameter into longitudinal (real) and transverse (imaginary) components is shown to be exact to linear order. The former does not couple with the wave vector (k) and frequency (ω) dependent external field, while the latter does. Explicit expressions are exhibited for the current and charge densities to leading order [ Δ T in the gap regime, in which Δτ s > 1 where τ s is the conduction electron spin flip lifetime; and Δ 2 T(ω + iDk 2) in the gapless regime, Δτ s < 1. D is the diffusion constant]. The continuity equation is shown to be obeyed to this order. Use of the Poisson equation in relation to the transverse component leads to a propagating mode, which, in the absence of magnetic impurities, reduces to the SS result. We find that the mode propagates only in the gap regime, whereas it is purely diffusive in the gapless regime and for gapless superconductors. In the presence of magnetic impurities, the solution reduces to the SS limit, but with reduced mode velocity and damping. The charge density appropriate to the propagating mode is shown to be zero to order ω ω p 2τ 1 , where τ 1 is the impurity scattering time and θ p the plasma frequency. The characteristic penetration length of an electric field into a superconductor is calculated, taking into account the phonon inelastic scattering time. The result reproduces the Waldram and SS expressions. Careful examination is made of the conditions under which these results pertain. The characteristic penetration length is also obtained in the gapless regime and for gapless superconductors for which T c τ s < 1. Finally, the longitudinal and transverse pair susceptibilities are calculated with and without magnetic impurities and in the gap and gapless regimes.

Betavoltaic energy conversion : L. C. Olsen, Donald W. Douglas Laboratories, Richland, Washington 99352, U.S.A. Energy Conversion13, 117–127 (1973)

We report here for the first time a fabrication of betavoltaic battery prototype consisting of 200 single conversion cells based on Schottky barrier diamond diodes which have been vertically stacked with ~24% 63Ni radioactive isotope. The maximum electrical output power of about 0.93 μW was obtained in total volume of 5 × 5 × 3.5 mm3. We used the ion-beam assisted lift-off technique to obtain conversion cells of minimal thickness comparable with the characteristic penetration length of beta-particles emitted by 63Ni isotope. The obtained value of 15 μm was limited by the mechanical strength of produced structures and process reliability. To check the performance of thin diamond based conversion cells we carried out IV-curves measurements at electron beam irradiation in SEM. We found that the sacrificial layer for the splitting of such thin conversion cell from HPHT diamond substrate did not cause a considerable degradation of device charge collection efficiency. As a result, the fabricated prototype provided the output power density of about 10 μW/cm3, that is the best known value for nuclear batteries based on 63Ni radioisotope. Moreover, the long half-life of 63Ni isotope gives the battery specific energy of about 3300 mWh/g that is an order of magnitude higher than the typical value of commercial chemical cells.